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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Subsemigroups of an amenable group


Author: Joe W. Jenkins
Journal: Proc. Amer. Math. Soc. 26 (1970), 226-227
MSC: Primary 20.93; Secondary 28.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0262405-2
MathSciNet review: 0262405
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Abstract: The following example is presented. $ G$ is a nondiscrete locally compact amenable group. $ H$ is a subgroup of $ G$ with zero Haar measure such that if $ g \in G \sim H$ then (i) there is a subsemigroup $ S = \bigcup\nolimits_{n = 0}^\infty {{I_n}}$ of $ G$ where the $ {I_n}'s$ are open pairwise disjoint ideals of $ S$ (all right- or all left-ideals) and (ii) $ g \in {I_0}$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0262405-2
Keywords: Amenable group, subsemigroup, open disjoint right(left-) ideals, free subsemigroup
Article copyright: © Copyright 1970 American Mathematical Society